Question

Mary must choose a new password where the first and last choices are possibly repeated lowercase letters; the second and third

Answer 1

The number of ways she can choose a password is 3986236800

In how many ways can she choose a password?

The given parameters and the possible selection of characters are:

First and last choices are possibly repeated lowercase letters;

There are 26 lower characters.

Since the characters can be repeated, then we have

First = 26

Last = 26

The second and third positions must be distinct uppercase letters

There are 26 upper characters.

Since the characters are distinct, then we have

Second = 26

Third = 25

The fourth position must be a # , $, or & symbol;

So, we have

Fourth = 3

The next four positions are distinct nonzero digits.

There are 9 nonzero digits.

Since the digits are distinct, then we have

Next = 9, 8, 7, 6

The number of ways she can choose a password is

Ways = First * Second * Third * Fourth * Next * Last

So, we have

Ways = 26 * 26 * 25 * 3 * 9 * 8 * 7 * 6 * 26

Evaluate the product

Ways = 3986236800

Hence, the number of ways she can choose a password is 3986236800

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